Simplify the following expression: $z = \dfrac{6x + 9}{8} \div \dfrac{8x}{10}$
Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{6x + 9}{8} \times \dfrac{10}{8x}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (6x + 9) \times 10 } { 8 \times 8x}$ $z = \dfrac{60x + 90}{64x}$ Simplify: $z = \dfrac{30x + 45}{32x}$